Smirnov is a "landowner in early middle age" according to the introduction we are given to him at the beginning of the play. He is bothering Mrs. Popov because her dead husband owed him a sum of money that he now needs to reclaim or else he will be in financial difficulties. He is a rather abrupt, rash man who comes across as very uncouth compared to the rather sophisticated Mrs. Popov. He is also very stubborn and straightforward, as his declaration to stay until he gets his money shows. Consider the following quote that he says:

It doesn't pay to wear kid gloves with this lot! All right, just you wait--I'll give you something to remember me by! You don't make a monkey out of me, blast you! I'm staying here--going to stick around till she coughs up. Pah! I feel well and truly riled today. I'm shaking like a leaf, I'm so furious--choking I am.

We can see from this quote that he is not afraid of expressing his emotions and that he is a very tenacious individual, determined to stay with Mrs. Popov until he gets his money. We can also infer that he is going to try to be as irritable as possible to ensure he gets his money as soon as he can, no matter how griefstricken Mrs. Popov is.